THE POSSIBLE ROLE OF MHD WAVES IN HEATING THE SOLAR CORONA

The possible role of waves in the heating of the solar corona has been investigated. A general dispersion relation has been derived for waves propagating in a homogeneous plasma subject to dissipation by viscosity and thermal conduction. The dissipation mechanisms have been incorporated self-consistently into the equations, and no assumptions about the strength of the damping have been made. Solutions of the sixth-order dispersion relation provide information on how the damping of both slow and fast mode waves depends upon the plasma density, temperature, field strength, and angle of propagation relative to the background magnetic field. We provide a detailed comparison to the standard approach, which is to solve for the wave quantities in the absence of dissipation and then to use these quantities in expressions for the heating due to viscosity and thermal conduction. It is possible that slow mode energy fluxes derived from Doppler line shift measurements in the chromosphere and transition region have been greatly underestimated, leading to the premature dismissal of slow mode waves in the literature. Specifically, Doppler line shift measurements do not account for unresolved, small-scale motions. Line broadening measurements, which do provide a way of estimating the amplitudes of small-scale motions, indicate that slow mode energy fluxes may be sufficient to meet the energy budget requirements of quiet regions. In fact, slow mode waves may also contribute to the heating in active regions, particularly if one considers that they may be generated in the corona by turbulent motions at magnetic reconnection sites. Calculations of wave damping rates from the dispersion relation for values representative of a quiet solar region indicate that slow mode waves with periods less than 300 s can damp sufficiently rapidly that they could dissipate enough energy to balance radiative losses. For active region conditions, slow mode waves with periods less than 100 s may provide adequate heating. Fast mode waves may also play an important role in coronal heating. Because fast mode wave group velocities are roughly an order of magnitude greater than those of slow mode waves, fast mode wave fluxes from below the corona can meet energy budget requirements in both quiet regions and active regions. For quiet region conditions, it was found that fast mode waves with periods less than about 75 s may damp at rates great enough to balance radiative losses. The damping of fast mode waves is inhibited by strong magnetic fields, and we find that only those waves with very high frequencies (tau < 1 s) can damp sufficiently rapidly to balance radiative losses in active regions. Although these frequencies are very high, there is no observational evidence that rules out their existence, and they may be generated both below the corona and at magnetic reconnection sites in the corona.